Vortex velocity pair correlations

The vortex velocity probability distribution for two distinct vortices is determined for the case of phase-ordering kinetics in systems with point defects. The n-vector model driven by time-dependent Ginzburg-Landau dynamics for a nonconserved order parameter is considered. The description includes the effects of other vortices and order-parameter fluctuations. At short distances the most probable configuration is that a vortex-antivortex pair has only a nonzero relative velocity that is inversely proportional to the distance between them. The coefficient of proportionality is determined explicitly.